The coefficient of restitution for the idealized impact of a spherical, nano-scale particle on a rigid plane

The theory of low velocity impact between nano-sized, spherical particles and a rigid plane is developed by assuming fully plastic failure during approach and assuming the Johnson Kandall Roberts model of elasticity and adhesion applied during particle recoil. This model predicts initial particle acceleration on approach, followed by either deceleration and eventually instantaneous cessation of particle motion or extreme deformation and possible structural failure of the particle. If the approach motion ceases and the recoil begins, then either the particle is trapped on the surface or it separates. The typical frequency of oscillations of trapped particles is derived. Criteria for the occurrence of the various regimes are derived, together with conditions for when surface adhesion is important.